Abstract
The training of a regression model depends on the purpose of the model. When a black-box model of dynamic systems is trained, two purposes are particularly common: prediction and simulation. The purpose of this paper is to highlight the differences between the learning of a dynamic-system model for prediction and for simulation in the presence of noise for Gaussian process models. Gaussian process models are probabilistic, nonparametric models that recently generated interest in the machine-learning community. This method can also be used also for the modelling of dynamic systems, which is the main interest of the engineering community. The paper elaborates the differences between prediction- and simulation-purposed modelling in the presence of noise, which is more difficult in the case when we train the model for simulation. An example is given to illustrate the described differences.
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References
Ažman, K., Kocijan, J.: Application of Gaussian processes for black-box modelling of biosystems. ISA Transactions 46, 443–457 (2007)
Gibbs, M.N.: Bayesian Gaussian Processes for Regression and Classification. Ph.d. thesis, Cambridge University (1997)
Henson, M.A., Seborg, D.E.: Adaptive nonlinear control of a pH neutralization process. IEEE Transactions on Control System Technology 2, 169–183 (1994)
Kocijan, J., Girard, A., Banko, B., Murray-Smith, R.: Dynamic systems identification with Gaussian processes. Mathematical and Computer Modelling of Dynamic Systems 11(4), 411–424 (2005)
Kocijan, J., Likar, B.: Gas-liquid separator modelling and simulation with Gaussian-process models. Simulation Modelling Practice and Theory 16(8), 910–922 (2008)
Ljung, L.: System identification – theory for the user, 2nd edn. Prentice Hall, New Jersey (1999)
Murray-Smith, R., Girard, A.: Gaussian Process priors with ARMA noise models. In: Proceedings of Irish Signals and Systems Conference, Maynooth, pp. 147–152 (2001)
Nelles, O.: Nonlinear System Identification. Springer, Heidelberg (2001)
Rasmusen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)
Sjoeberg, J., Zhang, Q., Ljung, L., Benveniste, A., Delyon, B., Glorennec, P.-Y., Hjalmarsson, H., Juditsky, A.: Nonlinear black-box modelling in system identification: A unified overview. Automatica 31(12), 1691–1724 (1995)
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Kocijan, J., Petelin, D. (2011). Output-Error Model Training for Gaussian Process Models. In: Dobnikar, A., Lotrič, U., Šter, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2011. Lecture Notes in Computer Science, vol 6594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20267-4_33
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DOI: https://doi.org/10.1007/978-3-642-20267-4_33
Publisher Name: Springer, Berlin, Heidelberg
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